Fuzzy Lattice Reasoning for Pattern Classification Using a New Positive Valuation Function

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="206121.fig.002a" src="https://static.hindawi.com/articles/afs/volume-2012/206121/figures/206121.fig.002a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b><svg height="13.55" id="M163" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 54.712502 13.55" width="54.712502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.55)">
<g transform="translate(72,-61.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜌</tspan>
<tspan style="font-size: 12.50px; " x="9.7398367" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.780226" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="28.031727" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="31.157476" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="37.408978" y="0">3</tspan>
</text>
</g>
</g>
</svg>: eight hyperboxes are generated </td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="206121.fig.002b" src="https://static.hindawi.com/articles/afs/volume-2012/206121/figures/206121.fig.002b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b><svg height="13.7375" id="M164" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 54.712502 13.7375" width="54.712502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.7375)">
<g transform="translate(72,-61.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜌</tspan>
<tspan style="font-size: 12.50px; " x="9.7398367" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.780226" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="28.031727" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="31.157476" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="37.408978" y="0">5</tspan>
</text>
</g>
</g>
</svg>: five hyperboxes are generated</td></tr></table></td></tr><tr class="fig-image" id="c"><td><img alt="206121.fig.002c" src="https://static.hindawi.com/articles/afs/volume-2012/206121/figures/206121.fig.002c.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(c) </b><svg height="13.55" id="M165" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 54.712502 13.55" width="54.712502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.55)">
<g transform="translate(72,-61.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜌</tspan>
<tspan style="font-size: 12.50px; " x="9.7398367" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.780226" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="28.031727" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="31.157476" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="37.408978" y="0">8</tspan>
</text>
</g>
</g>
</svg>: four hyperboxes are generated </td></tr></table></td></tr><tr class="fig-image" id="d"><td><img alt="206121.fig.002d" src="https://static.hindawi.com/articles/afs/volume-2012/206121/figures/206121.fig.002d.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(d) </b><svg height="13.55" id="M166" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 54.712502 13.55" width="54.712502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.55)">
<g transform="translate(72,-61.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜌</tspan>
<tspan style="font-size: 12.50px; " x="9.7398367" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.780226" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="28.031727" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="31.157476" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="37.408978" y="0">9</tspan>
</text>
</g>
</g>
</svg>: three hyperboxes are generated</td></tr></table></td></tr></table>

<table>Decision boundaries generated by the modified FLR with four different threshold parameters.</table>

Advances in Fuzzy Systems

fig2

Figure 2

Figure 2: Fuzzy Lattice Reasoning for Pattern Classification Using a New Positive Valuation Function 